Analytic models of the Rossiter-McLaughlin effect for arbitrary eclipser/star size ratios and arbitrary multiline stellar spectra

TL;DR

This paper develops an advanced analytic model for the Rossiter-McLaughlin effect that accounts for complex stellar spectra, arbitrary star-planet size ratios, and multiple spectral lines, improving accuracy over previous models.

Contribution

It introduces a comprehensive analytic framework that relaxes previous assumptions, incorporating the entire stellar spectrum and arbitrary size ratios, with applications to real observational data.

Findings

Model maintains accuracy for stellar rotation velocities up to 2-3 times the linewidth.

Application to HD 189733 yields a refined Rossiter-McLaughlin effect model.

Derived a lower estimate for the star's projected rotational velocity, Vsin i.

Abstract

We present an attempt to improve models of the Rossiter-McLaughlin effect by relaxing several restrictive assumptions. We consider the entire multiline stellar spectrum rather than just a single line, use no assumptions about the shape of the lines profiles, and allow arbitrary size ratio for the star and its eclipser. However, we neglect the effect of macro-turbulence and differential rotation. We construct our model as a power series in the stellar rotation velocity, $V\sin i$, giving a closed set of analytic formulae for up to three terms, and assuming quadratic limb-darkening law. We consider three major approaches of determining the Doppler shift: cross-correlation with a predefined template, cross-correlation with an out-of-transit stellar spectrum, and parametric modelling of the spectrum. A numerical testcase revels that our model preserves good accuracy for the rotation velocity of up to the limit of $2-3$ times the average linewidth in the spectrum. We also apply our approach to the Doppler data of HD 189733, for which we obtain an improved model of the Rossiter-McLaughlin effect with two correction terms, and derive a reduced value for $V\sin i$.